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The work investigates the geometric topological origins of particle mass, proposing new frameworks for understanding mass in physics.

March 24, 2026Open Access

On the Pure Geometric Topological Origin of Electron Mass and the Algebraic Reconstruction of the 64-State Mass Spectrum

Key Points

The work investigates the geometric topological origins of particle mass, proposing new frameworks for understanding mass in physics.
Utilized a 1+2 dimensional toroidal manifold of Arc Geometry.
Introduced a geometric topological impedance limit and absolute spatial scale.
Derived an electron mass baseline using algebraic methods.
Reconstructed the fundamental mass spectrum using a folding matrix and spatial modifiers.
Provided a standardized electron mass of approximately 0.510685 MeV/c².
Aligned the algebraic matrix with current collider data.
Indicated a ~ -0.06% shift in measured masses of heavy particles.
Expected the existence of two hidden eigenstates at a microscopic boundary.

Abstract

This manuscript explores the origin of particle mass through the lens of pure geometric topology, offering a theoretical alternative to the reliance on empirical parameters such as the measured speed of light (c) and the fine-structure constant () in the Standard Model. Grounded in the 1+2 dimensional toroidal manifold of Arc Geometry and the Law of Spontaneous Doubling (LSD), the study introduces a pure geometric topological impedance limit (₆₄₎₌^-1 137. 041286) and an absolute spatial scale (c₆₄₎ = 3 10⁸ m/s). Utilizing these geometric constants, an absolute standardized electron mass baseline is algebraically derived at M₀ₑ₂\䂰 0. 510685 MeV/c². By applying this baseline alongside a spatial asymmetrical projection modifier (P) to a topological folding matrix, the fundamental particle mass spectrum is reconstructed. The resulting algebraic matrix aligns closely with current collider data, while systematically indicating a -0. 06\% metrological shift in the measured masses of heavy particles (e. g. , the Top quark and Gauge bosons). Furthermore, guided by the 2⁶ topological eigen-surjection principle, the framework posits a 64-state topological architecture. This suggests a mathematical extension to the current 62-particle model, theoretically predicting the existence of two hidden eigenstates at the ultimate microscopic boundary: the Ran-Magnetic (Bₘ⁰) and Ran-Light (Bₗ⁰) poles. This work aims to provide a rigorous mathematical foundation for conceptualizing absolute topological evolution in theoretical physics.

On the Pure Geometric Topological Origin of Electron Mass and the Algebraic Reconstruction of the 64-State Mass Spectrum

Key Points

Abstract

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